Node weighted scheduling

This paper proposes a new class of online policies for scheduling in input-buffered crossbar switches. Given an initial configuration of packets at the input buffers, these policies drain all packets in the system in the minimal amount of time provided that there are no further arrivals. These policies are also throughput optimal for a large class of arrival processes which satisfy strong-law of large numbers. We show that it is possible for policies in our class to be throughput optimal even if they are not constrained to be maximal in every time slot.Most algorithms for switch scheduling take an edge based approach; in contrast, we focus on scheduling (a large enough set of) the most congested ports. This alternate approach allows for lower-complexity algorithms, and also requires a non-standard technique to prove throughput-optimality. One algorithm in our class, Maximum Vertex-weighted Matching (MVM) has worst-case complexity similar to Max-size Matching, and in simulations shows slightly better delay performance than Max-(edge)weighted-Matching (MWM).

Packet switching remains one of the bottlenecks in building fast Internet routers. Load balancing and switch scheduling are two important algorithms in the effort to maximize the throughput and minimize the latency of these packet switches. A load balancing algorithm regulates the traffic to conform to the service rates while a switch scheduling algorithm allocates the service rates adaptive to the arrival patterns. Many existing load balancing and switch scheduling algorithms are very similar. We show that load balancing and switch scheduling systems are dual systems based on the linear queue dynamics approximation. This allows us to cast a load balancing problem as a scheduling problem, and vice versa. We further show an example of designing a new algorithm for load balancing using an existing scheduling algorithm based on the duality. The duality perspective also allows us to solve unknown problems. We find the entropy rate of the randomized bandwidth allocation system with linear queue dynamics based on the knowledge of the entropy rate of the randomized load balancing system. For the general case, we find both an upper and a lower bound on the entropy rate. The joint use of dual load balancing and switch scheduling algorithms leads to performance gains as we show using mean field analysis.

An efficient iterative scheduling algorithm for input-queued switches, called round robin with longest queue first (RR/LQF), is proposed in this paper. RR/LQF consists of three phases: report, grant, and accept. In each phase, only a single-bit message per port is sent for reporting a packet arrival, granting an input for packet sending, or accepting a grant. In both the grant and accept phases, scheduling priority is given to the preferred input–output pairs first and the longest virtual output queuing (VOQ) next. The notion of the preferred input–output pair is to keep a global RR schedule among all the inputs and the outputs. By serving the preferred input–output pairs first, the match size tends to be maximized. By serving the longest VOQ next, the match weight is also boosted. When RR/LQF is executed for a single iteration (i.e., RR/LQF-1), we show by simulations that RR/LQF-1 outperforms all the existing single-bit-single-iteration scheduling algorithms. When RR/LQF is executed up to $N$ iterations (i.e., RR/LQF- $N$ ), we prove that under any admissible traffic pattern, RR/LQF- $N$ is stable with a speedup of $2-1/N$ , where $N$ is the switch size. To the best of our knowledge, this is the first work showing that an iterative scheduling algorithm is stable with a speedup less than 2. We then generalize RR/LQF to become a class of algorithms that have the same speedup bound of $2-1/N$ . Efforts are then made to further reduce the implementation complexity of RR/LQF. To this end, the pipelined RR/LQF and RR/RR, a simpler variant of RR/LQF, are proposed.

Scheduling algorithms for input-queued packet switches have been widely researched. It has been shown that various classes of scheduling algorithms provide guarantees on stability and on average delay for single switches. However, recent research has demonstrated that most of these scheduling algorithms do not guarantee stability for networks of switches. Most of the research that treats networks of switches proposes switching policies that require coordination among the single switches. The problem to find <i>distributed</i> scheduling policies that guarantee the stability of a network of switches has so far only been investigated for a policy based on a computationally very complex maximum weight matching algorithm. In this paper, we investigate <i>distributed</i> scheduling algorithms of <i>low complexity</i> that belong to the classes of maximal weight matching algorithms, <i>p</i>-maximal weight matching algorithms for switch architectures based on a space-division multiplexing extension, and MNCM algorithms. For these scheduling algorithms, we prove the stability of networks of input-queued switches where all switches deploy the same scheduling policy. We also show that networks of input-queued switches in which specific classes of different switching policies are deployed simultaneously at different switches are stable.

All-optical shared-buffer packet switches have been studied intensively in literature and many scheduling algorithms have been proposed. However, these algorithms either suffer from not being able to make resource reservation, or require high time-complexity to compute scheduling assignment for packets. In this paper, we propose a fast scheduling algorithm for all-optical shared-buffer packet switches. In our algorithm, packet scheduling is first formulated as a tree-searching problem. By breaking down the search tree into multiple smaller subsets and assigning each subset to a secondary processor, solutions can be obtained in a much shorter duration since the secondary processors are working in parallel. For instance, a scheduling assignment can be calculated for a packet in 55 ns with 8 processors, and in 25 ns with 64 processors, assuming a processor clock rate of 200 MHz. We show that our algorithm can achieve a loss rate of ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> even at load 0.9 for a 32times32 switch.

An evaluation of fair packet schedulers using a novel measure of instantaneous fairness

The delay and throughput characteristics of a packet switch depend mainly on the queueing scheme and the scheduling algorithm deployed at the switch. Early research on scheduling algorithms has mainly focused on maximum weight matching scheduling algorithms. It is known that maximum weight matching algorithms guarantee the stability of input-queued switches, but are impractical due to their high computational complexity. Later research showed that the less complex maximal matching algorithms can stabilize input-queued switches when they are deployed with a speed-up of two. For practical purposes, neither a high computational complexity nor a speed-up of two is desirable.In this paper, we investigate the application of matching algorithms that approximate maximum weight matching algorithms to scheduling problems. We show that while having a low computational complexity, they guarantee the stability of input queued switches when they are deployed with a moderate speed-up.In particular, we show that the improve_matching algorithm stabilizes input-queued switches when it is deployed with a speed-up of 3&lt;over&gt;2+ε.In a second step, we further improve on these results by proposing a class of maximal weight matching algorithms that stabilize an input-queued switch without any speed-up.Whereas initial research has only focused on scheduling algorithms that guarantee the stability of a single switch, recent work has shown how scheduling algorithms for single switches can be modified in order to design distributed scheduling algorithms that stabilize networks of input-queued switches. Using those results, we show that the switching algorithms proposed in this paper do not only stabilize a single switch, but also networks of input-queued switches.

SUMMARYOptical networks on chip based on silicon photonics have been proposed to reduce latency and power consumption in future chip multiprocessors. However, high performance chip multiprocessors use a shared memory model, which generates large numbers of short messages, creating high arbitration latency overhead for photonic switching networks. In this paper, we explore techniques that intelligently use information from the memory hierarchy to predict communication in order to setup photonic circuits with reduced or eliminated arbitration latency. Firstly, we present a switch scheduling algorithm, which arbitrates on a per memory transaction basis and holds open photonic circuits to exploit temporal locality. We show that this can reduce the average arbitration latency overhead by 60% and eliminate arbitration latency altogether for up to 70% of memory transactions. We then demonstrate that this switch scheduling algorithm operating with a central photonic crossbar or Clos switch has significant energy efficiency benefits over arbitration‐free photonic networks such as single writer multiple reader networks. Finally, we demonstrate that cache miss prediction can be used to predict 86% of more complex memory transactions involving multiple nodes or main memory. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Currently the research on input-queued ATM switches is one of the most active research fields. Many achievements have been made in the research on scheduling algorithms for unicast input-queued ATM switches and also applied in commerce. But the goal of the research on scheduling algorithms for multicast input-queued ATM switches only focuses on providing high throughput and inadvertently ignoring its undesired effects on QoS of the multicast traffic. In this paper we present a design scheme of input-queued ATM switches supporting multicast and corresponding scheduling algorithm, referred to as multicast longest normalized queue first (MLNQF). The MLNQF algorithm has the characteristics of improving throughput, satisfying QoS requirements and providing service fairly.

Static round-robin scheduling algorithms for scalable switches by Pun Kong Hong thesis 2002 vii, 48 leaves : ill. ; 30 cm The Clos-network is widely recognized as a scalable architecture for high-performance switches and routers. One of the key challenges…Read more ›

GENIUS – A genetic scheduling algorithm for high-performance switches

Cell-based input-queued crossbars are widely used in networking equipments. A number of crossbar scheduling algorithms have been proposed to provide high performance scheduling. It is critical for a crossbar scheduling algorithm to be fair and efficient in real world conditions, which include the presence of over-subscribed ingress ports and the possible flow control from the egress ports. Several commonly deployed algorithms are not fair when there are ingress congestions due to over-subscription. Furthermore, these algorithms lose fairness and can even cause starvation when there is flow control or backpressure from the egress ports. We illustrate the problems in detail using the well-known iSLIP algorithm. In this paper, we present a new algorithm, iSKIP, which performs as efficiently as iSLIP in a benign environment but remains fair and starvation-free in the cases of ingress congestion and egress backpressure. The iSKIP algorithm can be implemented in fast and simple hardware. Simulation results are presented to illustrate the advantages of the iSKIP algorithm.

This paper proposes a high-speed input and output buffering ATM switch, named the tandem-crosspoint (TDXP) switch. The TDXP switch consists of multiple crossbar switch planes. These switch planes are connected in tandem at all crosspoints. The TDXP switch architecture offers several advantages. First, the TDXP switch does not increase the internal line speed in eliminating head-of-line (HOL) blocking. Second, since the TDXP switch employs a simple cell reading algorithm at the input buffer in order to retain the cell sequence, the TDXP switch does not require the cell sequences to be rebuilt at output buffers using time stamps, as is required by a parallel switch. These merits make it easy to implement a high-speed ATM switch. Numerical results show that the TDXP switch can effectively eliminate HOL blocking and achieve high throughput. In addition, we discuss how TDXP switches can be combined to form larger switches in a cost-effective way. We clarify the relative advantages of the crossbar switch configuration and the three-stage Clos switch configuration in achieving a specific throughput. Because the three-stage Clos switch configuration is not strictly non-blocking, we introduce a nearly non-blocking condition and evaluate switch throughput under the condition. The evaluation shows that crossbar switch configuration becomes more cost effective as the throughput of individual switch LSIs, which depends on device technologies, increases.

We consider the problem of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quickest</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">detection</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">of</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">an</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intrusion</i> using a sensor network, keeping only a minimal number of sensors <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">active</i> . By using a minimal number of sensor devices, we ensure that the energy expenditure for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sensin</i> g, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">computation</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">communication</i> is minimized (and the lifetime of the network is maximized). We model the intrusion detection (or change detection) problem as a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Markov</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decision</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">process</i> (MDP). Based on the theory of MDP, we develop the following closed loop <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sleep/wake</i> scheduling algorithms: (1) optimal control of M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> , the number of sensors in the wake state in time slot k + 1, (2) optimal control of q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> , the probability of a sensor in the wake state in time slot k + 1, and an open loop <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sleep/wake</i> scheduling algorithm which (3) computes q, the optimal probability of a sensor in the wake state (which does not vary with time), based on the sensor observations obtained until time slot k. Our results show that an optimum closed loop control on M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> significantly decreases the cost compared to keeping any number of sensors active all the time. Also, among the three algorithms described, we observe that the total cost is minimum for the optimum control on M <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</i> and is maximum for the optimum open loop control on q.

Scheduling algorithm design is a critical and challenging issue in multiuser wireless networks with dynamic flows. The well-known Queue-length-based MaxWeight (QMW) scheduling algorithm can achieve throughput-optimality if there only exist persistent flows that are long-lived with infinite traffic arrival. In this paper, we propose a head-of-line access delay (HAD)-based scheduling algorithm and show that it is throughput-optimal when the flows are dynamic, i.e., they are short-lived with finite data to transmit. HAD is an online algorithm and does not require prior knowledge of the statistics of the arrival traffic and channel information. We also develop the Markov analytic model to study system performance and reveal important properties of the proposed HAD scheduling algorithm. To reduce the complexity of the analysis, we further study two approximation methods corresponding to different arrival traffic intensity. Performance evaluation shows that the HAD scheduling algorithm can outperform the classic QMW and stabilize the system at the presence of flow-level dynamics. Compared to the other existing algorithms, HAD is practical to implement with a better delay performance.